A disk-and-pin slotted-yoke mechanism converts rotation into straight reciprocation. A pin offset from the disk centre moves in a transverse slot. The guide lets the yoke follow one component of the pin’s circular path while the pin slides freely along the slot to accommodate the other.
Disk-and-Pin Alternate Rectilinear Interactive Calculator
Set the required stroke and starting disk angle. A crank pin stays inside the vertical slot of a yoke that moves on a horizontal guide. The result tiles show the selected angle; the animation displays current coordinates throughout a full turn.
Equation Used
- Crank pin radius equals half the required total stroke.
- Yoke travel is horizontal; pin sliding inside its slot is vertical.
- The pin remains inside the slot for the complete rotation.
- No clearance, compliance, friction or load deformation in the position calculation.
- Animation speed and structural proportions are explanatory, not design ratings.
The yoke has zero output velocity at the two stroke ends. Sinusoidal motion does not remove those reversal points. No speed, force, tolerance or fatigue rating is inferred.
A circular pin path and a straight output
The disk turns about a fixed shaft. Its crank pin traces a circle of radius r. The illustrated yoke has a vertical slot and is carried by a horizontal linear guide, so it can translate left and right without rotating.
The pin’s horizontal coordinate fixes the yoke position. Its vertical coordinate changes the location of contact along the slot. A sufficiently long slot keeps the pin captured at both vertical extremes.
The disk, yoke and guide hardware are shown in successive depth planes. The central bearing stand is behind the disk; it does not obstruct the guide carriage in front. Brown’s movement 93 shows this crank-pin-and-yoke principle with the output oriented vertically. Here it is turned for horizontal output.
Where the motion is useful
The arrangement is useful when one shaft turn should produce one complete straight reciprocation and a sinusoidal displacement is acceptable. It can explain the motion needed for a traverse, reciprocating member or small demonstrator.
Choosing it for a particular machine requires separate assessment of load, sliding contact, guides and wear. For a working traverse, match the slot, pin and guide design to the required stroke, speed and load.
Resolving the pin circle
With angle θ measured counterclockwise from the right-hand stroke end, the pin coordinates relative to the shaft are x = r cos θ and y = r sin θ. The yoke follows x, while y is the pin’s slide within the slot.
The extreme horizontal coordinates are +r and −r, giving total stroke S = 2r. Consequently, a required stroke determines r = S/2.
If the angular speed were a constant ω, the corresponding velocity would be −rω sin θ and acceleration −rω² cos θ. Output velocity is zero at the stroke ends, and the direction reverses there. The calculator here evaluates position; it does not assume a load or calculate drive torque.
A 50 mm output stroke
A 50 mm stroke requires a 25 mm crank-pin offset. At 0°, the yoke is at x = +25 mm and the pin is at the slot midpoint. At 90°, x = 0 and the pin is 25 mm above the midpoint.
At 180° the yoke reaches x = −25 mm. At 270° it returns to the central horizontal position with the pin 25 mm below the midpoint. At 360° it returns to the starting pose.
The numeric tiles remain a calculation for the selected angle. Autoplay adds a full revolution to that starting pose, and the diagram reports the changing coordinates separately.
Geometry is not a strength calculation
The slot and guide must accommodate the entire path. The animation includes space beyond the pin’s vertical extremes so it does not run into the slot ends. Its visible dimensions are illustrative rather than specified manufacturing clearances.
Real parts need suitable pin support, slot contact surfaces, lubrication, bearing alignment and strength. Their dimensions depend on actual loads and operation; the position formula alone does not establish tolerances, allowable rpm or service life.
Disk-and-pin questions
Is this the Scotch-yoke principle?
Yes. The circular crank-pin path acts through a straight transverse slot.
Why is the offset half the stroke?
The yoke moves between −r and +r, a distance of 2r.
Why does the pin move up and down while the carriage does not?
The slot permits that relative motion, while the linear guide constrains the carriage.
Are there reversal points?
Yes. Output velocity reaches zero at each stroke end before reversing.
Why do the live coordinates differ from the result tiles?
The tiles describe the selected starting angle. Autoplay advances the disk; the diagram shows that current pose.
Reference
Henry T. Brown, Five Hundred and Seven Mechanical Movements, Cornell University scan, movement 93, printed pages 28–29: crank pin working in a slotted yoke. The illustration here uses horizontal rather than vertical output.
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